Unbounded Operator Algebras and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Unbounded Operator Algebras and Representation Theory write by K. Schmüdgen. This book was released on 2013-11-11. Unbounded Operator Algebras and Representation Theory available in PDF, EPUB and Kindle. *-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the six ties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. J1'rom the very beginning, and still today, represen tation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particu lar, the theory of locally convex spaces, the theory of von Neumann algebras, distri bution theory, single operator theory, the momcnt problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject.
Lie algebras of unbounded operators
Lie algebras of unbounded operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie algebras of unbounded operators write by Palle E. T. Jørgensen. This book was released on 1980. Lie algebras of unbounded operators available in PDF, EPUB and Kindle.
Lie Algebras of Unbounded Operators
Lie Algebras of Unbounded Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Algebras of Unbounded Operators write by Isadore Manuel Singer. This book was released on 1950. Lie Algebras of Unbounded Operators available in PDF, EPUB and Kindle.
Lie Algebras of Bounded Operators
Lie Algebras of Bounded Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Algebras of Bounded Operators write by Daniel Beltita. This book was released on 2012-12-06. Lie Algebras of Bounded Operators available in PDF, EPUB and Kindle. In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras.
An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space
An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space write by Konrad Schmüdgen. This book was released on 2020-07-28. An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space available in PDF, EPUB and Kindle. This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.
